Problem: What do the following two equations represent? $2x-4y = 3$ $4x-8y = -3$
Answer: Putting the first equation in $y = mx + b$ form gives: $2x-4y = 3$ $-4y = -2x+3$ $y = \dfrac{1}{2}x - \dfrac{3}{4}$ Putting the second equation in $y = mx + b$ form gives: $4x-8y = -3$ $-8y = -4x-3$ $y = \dfrac{1}{2}x + \dfrac{3}{8}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.